Ergodicity, mixing, and existence of moments of a class of Markov models with applications to GARCH and ACD models
This paper studies a class of Markov models which consist of two components. Typically, one of the components is observable and the other is unobservable or 'hidden'. Conditions under which geometric ergodicity of the unobservable component is inherited by the joint process formed of the t...
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| Format: | Working paper |
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University of Oxford
2007
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| _version_ | 1826280799602737152 |
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| author | Meitz, M Saikkonen, P |
| author_facet | Meitz, M Saikkonen, P |
| author_sort | Meitz, M |
| collection | OXFORD |
| description | This paper studies a class of Markov models which consist of two components. Typically, one of the components is observable and the other is unobservable or 'hidden'. Conditions under which geometric ergodicity of the unobservable component is inherited by the joint process formed of the two components are given. This implies existence of initial values such that the joint process is strictly stationary and ?-mixing. In addition to this, conditions for the existence of moments are also obtained and extensions to the case of nonstationary initial values are provided. All these results are applied to a general model which includes as special cases various first order generalized autoregressive conditional heteroskedasticity (GARCH) and autoregressive conditional duration (ACD) models with possibly complicated non-linear structures. The results only require mild moment assumptions and in some cases provide necessary and sufficient conditions for geometric ergodicity. |
| first_indexed | 2024-03-07T00:19:09Z |
| format | Working paper |
| id | oxford-uuid:7be9c1c3-f288-4dfb-9412-d7e46c4cca25 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T00:19:09Z |
| publishDate | 2007 |
| publisher | University of Oxford |
| record_format | dspace |
| spelling | oxford-uuid:7be9c1c3-f288-4dfb-9412-d7e46c4cca252022-03-26T20:53:45ZErgodicity, mixing, and existence of moments of a class of Markov models with applications to GARCH and ACD modelsWorking paperhttp://purl.org/coar/resource_type/c_8042uuid:7be9c1c3-f288-4dfb-9412-d7e46c4cca25Bulk import via SwordSymplectic ElementsUniversity of Oxford2007Meitz, MSaikkonen, PThis paper studies a class of Markov models which consist of two components. Typically, one of the components is observable and the other is unobservable or 'hidden'. Conditions under which geometric ergodicity of the unobservable component is inherited by the joint process formed of the two components are given. This implies existence of initial values such that the joint process is strictly stationary and ?-mixing. In addition to this, conditions for the existence of moments are also obtained and extensions to the case of nonstationary initial values are provided. All these results are applied to a general model which includes as special cases various first order generalized autoregressive conditional heteroskedasticity (GARCH) and autoregressive conditional duration (ACD) models with possibly complicated non-linear structures. The results only require mild moment assumptions and in some cases provide necessary and sufficient conditions for geometric ergodicity. |
| spellingShingle | Meitz, M Saikkonen, P Ergodicity, mixing, and existence of moments of a class of Markov models with applications to GARCH and ACD models |
| title | Ergodicity, mixing, and existence of moments of a class of Markov models with applications to GARCH and ACD models |
| title_full | Ergodicity, mixing, and existence of moments of a class of Markov models with applications to GARCH and ACD models |
| title_fullStr | Ergodicity, mixing, and existence of moments of a class of Markov models with applications to GARCH and ACD models |
| title_full_unstemmed | Ergodicity, mixing, and existence of moments of a class of Markov models with applications to GARCH and ACD models |
| title_short | Ergodicity, mixing, and existence of moments of a class of Markov models with applications to GARCH and ACD models |
| title_sort | ergodicity mixing and existence of moments of a class of markov models with applications to garch and acd models |
| work_keys_str_mv | AT meitzm ergodicitymixingandexistenceofmomentsofaclassofmarkovmodelswithapplicationstogarchandacdmodels AT saikkonenp ergodicitymixingandexistenceofmomentsofaclassofmarkovmodelswithapplicationstogarchandacdmodels |